## Symmetry Reduction for SAT Representations of Transition Systems

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Citations: | 17 - 1 self |

### BibTeX

@MISC{Rintanen_symmetryreduction,

author = {Jussi Rintanen},

title = {Symmetry Reduction for SAT Representations of Transition Systems},

year = {}

}

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### Abstract

Symmetries are inherent in systems that consist of several interchangeable objects or components. When reasoning about such systems, big computational savings can be obtained if the presence of symmetries is recognized. In earlier work, symmetries in constraint satisfaction problems have been handled by introducing symmetry-breaking constraints.

### Citations

1116 | Chaff: Engineering an Efficient SAT Solver
- Moskewicz, Madigan, et al.
- 2001
(Show Context)
Citation Context ...9 step problem instance with 20 balls has 9756 propositions and 304538 clauses. Satisfiability problems this big can be very difficult to solve. The runtimes are for the ZChaff satisfiability solver (=-=Moskewicz et al. 2001-=-) and are given in seconds of CPU time (we also tried other solvers like relsat, satz and SATO that are slower on these problems, satz and SATO often very much slower.) The problem instances are from ... |

522 | Pushing the envelope: planning, propositional logic, and stochastic search
- Kautz, Selman
- 1201
(Show Context)
Citation Context ...the state space. Satisfiability testing in the propositional logic has been used as a computational framework for solving a number of problems about transition systems. In planning by satisfiability (=-=Kautz & Selman 1996-=-) and its extensions (Rintanen 1999; Majercik & Littman 1999), sequences of actions/transitions are represented in the classical propositional logic or its quantified extensions. Similarly, bounded mo... |

185 | Better verification through symmetry - Ip, Dill - 1993 |

167 | P.: Symmetry and model checking
- Emerson, Sistla
- 1996
(Show Context)
Citation Context ...ed. 1991). Similarly, model-checking algorithms for temporal logics have been modified to work on the quotient structure resulting from identification of states that are equivalent modulo symmetries (=-=Emerson & Sistla 1996-=-). These techniques solve the symmetry reduction problem for planning algorithms that use plain backward or forward search in the state space. Satisfiability testing in the propositional logic has bee... |

158 | A.: Symmetry-breaking predicates for search problems
- Crawford, Ginsberg, et al.
- 1996
(Show Context)
Citation Context ...n addressed in earlier work. We present a solution to the problem. Introduction Symmetry breaking has been extensively investigated in connection with problems represented in the propositional logic (=-=Crawford et al. 1996-=-; Joslin & Roy 1997). Symmetries divide the set of all solutions to equivalence classes: two symmetric solutions belong to the same equivalence class. The standard way of utilizing symmetries is by so... |

148 | B.: Encoding plans in propositional logic - Kautz, McAllester, et al. - 1996 |

141 | Constructing Conditional Plans by a Theorem-Prover
- Rintanen
- 1999
(Show Context)
Citation Context ...n the propositional logic has been used as a computational framework for solving a number of problems about transition systems. In planning by satisfiability (Kautz & Selman 1996) and its extensions (=-=Rintanen 1999-=-; Majercik & Littman 1999), sequences of actions/transitions are represented in the classical propositional logic or its quantified extensions. Similarly, bounded model-checking (Biere et al. 1999) re... |

130 |
Eliminating interchangeable values in constraint satisfaction problems
- Freuder
- 1991
(Show Context)
Citation Context ...ce symmetric transition systems has been proposed by Ip and Dill (1996). Interchangeability of objects has been pointed as a main source/consequence of symmetries in constraint satisfaction problems (=-=Freuder 1991-=-), and this has been taken advantage of for example by Joslin and Roy (1997) in computing symmetries for different types of constraint satisfaction problems, including planning, from schematic descrip... |

59 | M.L.: Contingent planning under uncertainty via stochastic satisfiability
- Majercik, Littman
- 2003
(Show Context)
Citation Context ...onal logic has been used as a computational framework for solving a number of problems about transition systems. In planning by satisfiability (Kautz & Selman 1996) and its extensions (Rintanen 1999; =-=Majercik & Littman 1999-=-), sequences of actions/transitions are represented in the classical propositional logic or its quantified extensions. Similarly, bounded model-checking (Biere et al. 1999) represents transition seque... |

53 | D.: The detection and exploitation of symmetry in planning problems
- Fox, Long
- 1999
(Show Context)
Citation Context ...ak only the symmetries at the first time point. 2 For a certain set of problems they show that even this restricted form of symmetry breaking leads to big efficiency gains. Some planning researchers (=-=Fox & Long 1999-=-; Guéré & Alami 2001; Fox & Long 2002) have published papers on symmetry reduction techniques that are less general and less powerful than earlier state-of-the-art symmetry reduction techniques. Guere... |

43 |
Reachability analysis of Petri nets using symmetries
- Starke
- 1991
(Show Context)
Citation Context ...f states, a set T of transition relations t ⊆ S × S, 1 and a set I ⊆ S of initial states. We now define symmetries. Our definitions are similar or equivalent to those used earlier work on symmetries (=-=Starke 1991-=-; Emerson & Sistla 1996). A main difference to much of the earlier work is that the transition between two states has to be mapped to a symmetric transition. This labeling of the arcs in the transitio... |

27 |
Exploiting symmetry in lifted csps
- Joslin, Roy
- 1997
(Show Context)
Citation Context ... work. We present a solution to the problem. Introduction Symmetry breaking has been extensively investigated in connection with problems represented in the propositional logic (Crawford et al. 1996; =-=Joslin & Roy 1997-=-). Symmetries divide the set of all solutions to equivalence classes: two symmetric solutions belong to the same equivalence class. The standard way of utilizing symmetries is by socalled symmetry-bre... |

24 | Extending the exploitation of symmetries in planning - Fox, Long - 2002 |

9 | Exploiting symmetry when modelchecking software. In Formal Methods for Protocol Engineering and Distributed Systems - Godefroid - 1999 |

9 | One action is enough to plan - Guere, Alami - 2001 |